The chart begins with a simple major third interval such as C-E as the
basis of a "tonic" major triad (I). This is done because preparation for
tritonic reflex originates in the major third (or an inverted minor sixth),
reflexing to a tritone contained in a chord configuration. The tendency is for
the altered tones to continue in the same direction, reflexing to the tones of
a new major third interval. The "tonic" box above contains the scales within
the Chromatic Key as represented by the chord composed of each scale's primary
tones. Indicated chord configurations assume the possibility of added or
subtracted tones for variety of harmonic density. The root and third of I (the
tonic major triad, respelled IIIm+) are also present in IM7, VIm (respelled
IM6), and I7 (respelled IIIo(b13)).
Root of I might as well be D as C, or any other of the twelve possible
tones. The relationships remain the same. For example, if root of I is Db
instead of C, then VIm is Bbm instead of Am. V7 is Ab7 instead of G7 and so
forth.
At any point along a proposed course, a progression, however,
relationships, or the course itself, may be altered from the proposed
"perfect" tritonic progression. The chart indicates, for example, that the
tritonic preparation which finds C descending to B and the E ascending to F
simultaneously forming the reflexing tritone, may occur in two steps, as
represented by the Ascending Transition box: C remains stationary as E
ascends to F. The result may be the traditional Subdominant, IV (respelled
VIm+). When the C finally completes the remainder of the transition to B, the
result may be recognized as V7, the traditional dominant seventh (respelled
here as VIIo(b13)). B and F, however, may also be constituents of bII7 or
IVo7, with similar dominant quality, but of altered effect. Additionally,
bII7 may be respelled as IVo(b13) for another variation in dominant effect,
and IVo7 as VIIo7, bVIo7, or IIo7.
The resulting dominant chord (or scale), instead of resolving as
expected to I as tonic, may resolve with tritonic reflex in consistent
direction to bV, to bIIIm, to bV7, to bV+, to bVM7, or to bVIIm+, bVM6, or
bVIIo(b13), respellings of the more direct configurations.
Rather than resolving directly to bV or its relatives, however, V7 may
also follow a similar pattern of ascending transition to VII, VIIm, VM7,
bVIm7, or one of their respellings, bIIIm+, IIM6, or VIIM6, then on to bV,
here called the Remote Tonic-Subdominant. V7 may follow the less "strong"
course of the descending transition to bVM7, bVII, bVIIm (which is similar
to the Remote Tonic-Subdominant in effect), or to either of their respellings,
IIm+ and bIIM6.
At some point along any of these possible courses, a configuration of
tonic quality may be treated as new tonic (a major triad, a major seventh, a
major sixth, a minor triad, a minor augmented triad, a diminished flat
thirteenth, or even a dominant seventh chord. If so, another, totally
surprising sequence, moves into a related "region" of Chromatic Key with the
new tonic as key center. Relative nearness of relationships among regions of
Chromatic Key centers becomes a moot point unless the composer purposely
restricts the 12-tone scale, creating secondary configurations resembling
diatonic scales. In this event, scales with the most tones in common are
closest and those with the least tones in common are more remote as in
Schoenberg's "regions."
Many of the functional root/configurations in the above chart are
altered (transformations) from strict chromatic key. If one wishes to quickly
"touch base" with chromatic key configurations to avoid the illusion of having
wandered into diatonic regions, one may resolve the functional configuration
to the chromatic key scale before progressing to a functional scale and
proceeding.
In general, the suggested resolutions and their
succeeding progressions allow one or more tones
moving by half-steps to continue moving in the same
direction and manner to a root that is in relative line of
function. Tones moving upward will tend to describe
new roots. Tones moving downward will tend to
describe new major thirds.
Using alternate root spellings for diminished and augmented
configurations, the original function chart yields forty-nine
root/configurations, utilizing each of the twelve tones from two to six times
in various functionalities. Not all possible configurations are indicated.
We may therefore assume that roots and configurations may be considered as
relatively separate entities. In general, progressions may move from relative
tonic or subdominent function to dominant and back to tonic--or to remote
tonic directly or through double-subdominant (the ascending transition)--
however, any root found in any functionality box, regardless of associated
configuration may be considered as of the functionality indicated.
By the same token, any configuration found in any box may be
considered to be of the relative functionality indicated. Note that some
configurations are of vague functionality. Diminished flat-thirteenth, for
example, is essentially a respelling of the dominant seventh, but may be
found as a "relative" tonic. If unprepared, I7 will be a weak tonic
suggesting secondary dominance, reflexing to the fifth below. Special
circumstances of context, however, may emphasize an autonomous tonic
character. A repetitive dominant-tonic codetta form, for example, may be
used to emphasize tonic effect. The major seventh and major sixth arrive at
their tonic characteristic by simply stopping before ultimate resolution to
the absolute tonic triad. We have become accustomed to M7 and M6 as tonic
configurations rather than as relative minor and as tonic suspension, which
is what they really are. Major sixth and major seventh chords actually
function on every level but dominant. Minor augmented, likewise, is a
respelled major triad and may, therefore, be used as any functionality.
Altered chords, transformations, suspensions, and the like function as they
resolve and are, therefore, relatively of the same function as the chord to
which they resolve, especially of the two configurations have the same tone
as tonic. An example progression might be:
(I - IV - V(7)) - (IIIm - VIm - VIIo7) - (VII - bV) - (IVo7 - bIIIm - bVIIm)
- (V7 - I)
This relatively simple progression moves from simple tonic to
subdominant to dominant, then, using respelled roots, it makes the same
circuit to dominant again, then by ascending transition to remote
tonic/subdominant, another round of respelled roots from dominant/ascending
transition/remote tonic to obvious dominant, to absolute tonic. This method
of progression design incorporates repetition with variation within
functional form.
If one adds an occasional Chromatic Key "touchstone," to the above
progression and a couple key center "modulations," something similar to the
following may develop. (Chromatic Key "touchstones" are in brackets,
functional cycles are in parentheses):
key center--C: (I - IV - V(7)) - (IIIm -VIm - VIIo7 - [VII/7] ) -
(VII7 - bV - [bV/7] - bVI ) - (IVo7 - bIIIm - [bIIIM7+] - I+ - bVIIm7) -
(V7 - I(7)) F: (I - IV(7) - V(7)) - (IIIm - IIm - VIIo7 - [VII/7] ) -
(VII7 - bV - [bV/7] - bII) - (IVo7 - IV7 - Eb: I - I+) G: (I - IV - V(7)) -
(I) (M7 - 7) C: (I)
As mentioned earlier, any root may be treated as tonic (I), ignoring
the configuration and its function shown on the chart. This is especially
true if the preceding chord is transformed to a configuration of relative
dominance to the new root as tonic. With each change of
key center, one accesses a fresh "layer" of the modal continuum. In the above
progression, for example, the ultimate I (C in the first section is altered
to I7 (C7, which reflexes to F as I. A little later IVo7 is altered to IV7,
which reflexes to Eb as I. Eb becomes remote tonic Eb+, and a new tonic, G,
appears from nowhere in particular. G moves through the simple cadencial
motif, I - IV - V7 - I, then I becomes IM7-(7), resolving finally to C, the
original tonic. All this is rather prosaic. Much more inventive progressions
are possible.
The augmented triad is indicated as a "Remote Tonic." The augmented
triad has long been used for this special effect. Now we have a functional
name for the effect, which essentially escapes conventional tonality by
using a configuration not directly identifiable with a particular tonal
orientation. The new designation indicates not only actual function, but
potential function.
Schoenberg suggests that all diminished chords are subdominant in
effect. This chart indicates that IVo7 (which may be respelled bVIo7, VIIo7,
or IIo7 and their enharmonic spellings) is potentially relatively dominant in
effect, especially if the root, approached by ascending half-step, resolves
upward a half step to the new root.
The above understanding of scale relationships within Chromatic Key
clearly explains traditional "strong" function and introduces additional
resources of relative (or remote) function with expanded varieties of effect.
The above relationships are, furthermore, based on actual tonal relationships
rather than on mere conventional usage.
© Dwight Winenger 1996
09/28/06